BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CMSA - ECPv6.16.3//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-ORIGINAL-URL:https://cmsa.fas.harvard.edu X-WR-CALDESC:Events for CMSA REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:America/New_York BEGIN:DAYLIGHT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:EDT DTSTART:20200308T070000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST DTSTART:20201101T060000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:EDT DTSTART:20210314T070000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST DTSTART:20211107T060000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:EDT DTSTART:20220313T070000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST DTSTART:20221106T060000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:EDT DTSTART:20230312T070000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST DTSTART:20231105T060000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=America/New_York:20221027T103000 DTEND;TZID=America/New_York:20221027T113000 DTSTAMP:20260707T094147 CREATED:20230817T180439Z LAST-MODIFIED:20240118T090238Z UID:10001246-1666866600-1666870200@cmsa.fas.harvard.edu SUMMARY:Gravitational Wave\, Angular Momentum\, and Supertranslation Ambiguity DESCRIPTION:General Relativity Seminar \n\nSpeaker: Naqing Xie (Fudan University) \nTitle: Gravitational Wave\, Angular Momentum\, and Supertranslation Ambiguity\n\nAbstract: The supertranslation ambiguity of angular momentum is a long-standing and conceptually important issue in general relativity. Recently\, there appeared the first definition of angular momentum at null infinity that is supertranslation invariant. However\, in the compact binary coalescence community\, supertranslation ambiguity is often ignored. We have shown that\, in the linearised theory of gravitational wave\, the new angular momentum coincides with the classical definition at the quadrupole level. This talk is based on a recent joint work with Xiaokai He and Xiaoning Wu. URL:https://cmsa.fas.harvard.edu/event/gr_102722/ LOCATION:Virtual CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20221020T103000 DTEND;TZID=America/New_York:20221020T113000 DTSTAMP:20260707T094147 CREATED:20240215T103645Z LAST-MODIFIED:20240229T093550Z UID:10002742-1666261800-1666265400@cmsa.fas.harvard.edu SUMMARY:Love Symmetry of Black Holes DESCRIPTION:General Relativity Seminar \nSpeaker: Sergei Dubovsky (New York University)\n\n\n\nTitle: Love Symmetry of Black Holes\n\n\nAbstract: Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2\,ℝ) symmetry in the suitably defined near zone approximation. We show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2\,ℝ) representation theory. In particular\, static perturbations of four-dimensional black holes belong to highest weight SL(2\,ℝ) representations. It is this highest-weight property that forces the static Love numbers to vanish. We show that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. The Love symmetry also exhibits a peculiar UV/IR mixing. URL:https://cmsa.fas.harvard.edu/event/gr_102022/ LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States CATEGORIES:General Relativity Seminar ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-10.20.22.png END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20221013T103000 DTEND;TZID=America/New_York:20221013T233000 DTSTAMP:20260707T094147 CREATED:20240215T091921Z LAST-MODIFIED:20240229T092506Z UID:10002712-1665657000-1665703800@cmsa.fas.harvard.edu SUMMARY:Strong Cosmic Censorship DESCRIPTION:General Relativity Seminar \n\nSpeaker: Professor Oscar Dias (University of Southampton) \n\nTitle: Strong Cosmic Censorship \nAbstract: Generically\, strong cosmic censorship (SCC) is the statement that physics within general relativity should be predicted from initial data prescribed on a Cauchy hypersurface. In this talk I will review how fine-tuned versions of SCC have been formulated and evolved along the last decades up to the point where we believe that Christodoulou’s version is true in asymptotically flat spacetimes. However\, I will also describe that in recent years it was found that this is no longer necessarily true for some other backgrounds\, namely in some de Sitter (with a positive cosmological constant) spacetimes or even in rotating BTZ black holes in 3-dimensional Anti-de Sitter spacetime. Finally\, I will discuss some possibilities (quantum effects\, non-smooth initial data\,…) that might restore SCC in those backgrounds where the standard formulation of the conjecture is violated. URL:https://cmsa.fas.harvard.edu/event/gr_101322/ LOCATION:Virtual CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20221006T103000 DTEND;TZID=America/New_York:20221006T233000 DTSTAMP:20260707T094147 CREATED:20240215T092242Z LAST-MODIFIED:20240229T092649Z UID:10002715-1665052200-1665099000@cmsa.fas.harvard.edu SUMMARY:Duality in Einstein’s Gravity DESCRIPTION:General Relativity Seminar \nSpeaker: Uri Kol\, CMSA \n\nTitle: Duality in Einstein’s Gravity \nAbstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals\, in turn\, a wide range of new IR phenomena\, including aspects of the double copy for scattering amplitudes\, asymptotic symmetries and more. URL:https://cmsa.fas.harvard.edu/event/gr_10622/ LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220929T103000 DTEND;TZID=America/New_York:20220929T113000 DTSTAMP:20260707T094147 CREATED:20240216T091125Z LAST-MODIFIED:20240229T111436Z UID:10002755-1664447400-1664451000@cmsa.fas.harvard.edu SUMMARY:General-relativistic viscous fluids DESCRIPTION:General Relativity Seminar \nSpeaker: Marcelo Disconzi\, Vanderbilt University \nTitle: General–relativistic viscous fluids\n\nAbstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions\, as the quark-gluon plasma is the hottest\, smallest\, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe\, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades\, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments\, theory\, phenomenology\, and numerical simulations. From these investigations\, a coherent picture has emerged\, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently\, state-of-the-art numerical relativity simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems\, a robust and comprehensive theory of relativistic fluids with viscosity is still lacking. This is due\, in part\, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk\, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues. URL:https://cmsa.fas.harvard.edu/event/general-relativistic-viscous-fluids/ LOCATION:Virtual CATEGORIES:General Relativity Seminar ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-09.29.22.png END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220922T103000 DTEND;TZID=America/New_York:20220922T113000 DTSTAMP:20260707T094147 CREATED:20240216T113602Z LAST-MODIFIED:20240229T110700Z UID:10002767-1663842600-1663846200@cmsa.fas.harvard.edu SUMMARY:A scale-critical trapped surface formation criterion for the Einstein-Maxwell system DESCRIPTION:General Relativity Seminar \n\n\nSpeaker: Nikolaos Athanasiou\n\nTitle: A scale-critical trapped surface formation criterion for the Einstein-Maxwell system\n\nAbstract: Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution\, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences\, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result\, in collaboration with Xinliang An\, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system. URL:https://cmsa.fas.harvard.edu/event/a-scale-critical-trapped-surface-formation-criterion-for-the-einstein-maxwell-system/ LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States CATEGORIES:General Relativity Seminar ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-09.22.22.png END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220915T103000 DTEND;TZID=America/New_York:20220915T113000 DTSTAMP:20260707T094147 CREATED:20240214T111637Z LAST-MODIFIED:20240229T104038Z UID:10002693-1663237800-1663241400@cmsa.fas.harvard.edu SUMMARY:The Gregory-Laflamme instability of black strings revisited DESCRIPTION:General Relativity Seminar\n\nTitle: The Gregory-Laflamme instability of black strings revisited\n \nAbstract: In this talk I will discuss our recent work that reproduces and extends the famous work of Lehner and Pretorius on the end point of the Gregory-Laflamme instability of black strings. We consider black strings of different thicknesses and our numerics allow us to get closer to the singularity than ever before. In particular\, while our results support the picture of the formation of a naked singularity in finite asymptotic time\, the process is more complex than previously thought. In addition\, we obtain some hints about the nature of the singularity that controls the pinch off of the string. URL:https://cmsa.fas.harvard.edu/event/title-tba-3/ LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States CATEGORIES:General Relativity Seminar ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-09.15.22-1.png END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220908T103000 DTEND;TZID=America/New_York:20220908T113000 DTSTAMP:20260707T094147 CREATED:20240214T105852Z LAST-MODIFIED:20240301T084331Z UID:10002689-1662633000-1662636600@cmsa.fas.harvard.edu SUMMARY:The second law of black hole mechanics in effective field theory DESCRIPTION:General Relativity Seminar \nSpeaker: Professor Harvey Reall (University of Cambridge)  \nTitle: The second law of black hole mechanics in effective field theory \nAbstract: I shall discuss the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. I shall explain how this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations\, provided that one treats the higher derivative terms in the sense of effective field theory. This talk is based on work with Stefan Hollands and Aron Kovacs. \nVideo URL:https://cmsa.fas.harvard.edu/event/the-second-law-of-black-hole-mechanics-in-effective-field-theory/ LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220428T153500 DTEND;TZID=America/New_York:20220428T163500 DTSTAMP:20260707T094147 CREATED:20240301T114205Z LAST-MODIFIED:20240301T114205Z UID:10002896-1651160100-1651163700@cmsa.fas.harvard.edu SUMMARY:A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter DESCRIPTION:Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk\, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability. URL:https://cmsa.fas.harvard.edu/event/4-28-2022-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220421T100000 DTEND;TZID=America/New_York:20220421T110000 DTSTAMP:20260707T094147 CREATED:20240214T095030Z LAST-MODIFIED:20240301T114330Z UID:10002648-1650535200-1650538800@cmsa.fas.harvard.edu SUMMARY:Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system DESCRIPTION:Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability\, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof\, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover\, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument. URL:https://cmsa.fas.harvard.edu/event/4-21-2022-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220414T093000 DTEND;TZID=America/New_York:20220414T103000 DTSTAMP:20260707T094147 CREATED:20240214T083016Z LAST-MODIFIED:20240301T112943Z UID:10002589-1649928600-1649932200@cmsa.fas.harvard.edu SUMMARY:Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4 DESCRIPTION:Abstract: In this talk\, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang. URL:https://cmsa.fas.harvard.edu/event/4-14-2022-general-relativity-seminar/ LOCATION:Virtual CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220328T130000 DTEND;TZID=America/New_York:20220328T140000 DTSTAMP:20260707T094147 CREATED:20240214T082503Z LAST-MODIFIED:20240301T113123Z UID:10002586-1648472400-1648476000@cmsa.fas.harvard.edu SUMMARY:Black Hole Spectroscopy DESCRIPTION:Abstract: According to general relativity\, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes\, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as\, say\, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy? URL:https://cmsa.fas.harvard.edu/event/3-28-2022-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220324T093000 DTEND;TZID=America/New_York:20220324T103000 DTSTAMP:20260707T094147 CREATED:20240214T082228Z LAST-MODIFIED:20240301T113314Z UID:10002585-1648114200-1648117800@cmsa.fas.harvard.edu SUMMARY:Rough solutions of the $3$-D compressible Euler equations DESCRIPTION:Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D\, for the Cauchy data of the velocity\, density and vorticity $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $22$. At the opposite extreme\, in the incompressible case\, i.e. with a constant density\,  the result is known to hold for $\omega\in H^s$\, $s>3/2$ and fails for $s\le 3/2$\, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $s>2\, \\, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves\, governed by quasilinear wave equations\, and vorticity which is transported by the flow. To overcome this difficulty\, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime. URL:https://cmsa.fas.harvard.edu/event/3-24-2022-general-relativity-seminar/ CATEGORIES:General Relativity Seminar ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.24.22-2.png END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220321T130000 DTEND;TZID=America/New_York:20220321T140000 DTSTAMP:20260707T094147 CREATED:20240214T081657Z LAST-MODIFIED:20240813T160939Z UID:10002584-1647867600-1647871200@cmsa.fas.harvard.edu SUMMARY:Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes DESCRIPTION:Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation\, we prove rigorous mathematical statements toward this conjecture. \nIn particular\, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result\, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes. \nThis is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas). URL:https://cmsa.fas.harvard.edu/event/3-21-2022-general-relativity-seminar/ CATEGORIES:General Relativity Seminar ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.21.22.png END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220310T130000 DTEND;TZID=America/New_York:20220310T140000 DTSTAMP:20260707T094147 CREATED:20240214T080539Z LAST-MODIFIED:20240813T160832Z UID:10002579-1646917200-1646920800@cmsa.fas.harvard.edu SUMMARY:The Einstein-flow on manifolds of negative curvature DESCRIPTION:Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes\, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations\, how they can be handled depending on the matter model at hand\, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions. URL:https://cmsa.fas.harvard.edu/event/3-10-2022-general-relativity-seminar/ CATEGORIES:General Relativity Seminar ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.10.22.png END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220224T130000 DTEND;TZID=America/New_York:20220224T140000 DTSTAMP:20260707T094147 CREATED:20240214T080100Z LAST-MODIFIED:20240304T051713Z UID:10002576-1645707600-1645711200@cmsa.fas.harvard.edu SUMMARY:Extreme Black Holes: Anabasis and Accidental Symmetry DESCRIPTION:  \n \n  \nSpeaker: Achilleas Porfyriadis\, Harvard Black Hole Initiative \nTitle: Extreme Black Holes: Anabasis and Accidental Symmetry \nAbstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2)transformation properties of the spherically symmetric linear perturbations of  AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2\, with or without additional matter\, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of AdS_2. URL:https://cmsa.fas.harvard.edu/event/2-24-2022-general-relativity-seminar/ LOCATION:Virtual CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220217T130000 DTEND;TZID=America/New_York:20220217T140000 DTSTAMP:20260707T094147 CREATED:20240214T075908Z LAST-MODIFIED:20240304T052235Z UID:10002574-1645102800-1645106400@cmsa.fas.harvard.edu SUMMARY:Black Hole dynamics at Large D DESCRIPTION:Abstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics\, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime. URL:https://cmsa.fas.harvard.edu/event/2-17-2022-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20220210T093000 DTEND;TZID=America/New_York:20220210T103000 DTSTAMP:20260707T094147 CREATED:20240304T103339Z LAST-MODIFIED:20240304T103339Z UID:10002899-1644485400-1644489000@cmsa.fas.harvard.edu SUMMARY:Dihedral ridigity and mass DESCRIPTION:Abstract: To characterise scalar curvature\, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk\, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass). URL:https://cmsa.fas.harvard.edu/event/2-10-2022-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211216T130000 DTEND;TZID=America/New_York:20211216T140000 DTSTAMP:20260707T094147 CREATED:20240214T075612Z LAST-MODIFIED:20240304T052540Z UID:10002573-1639659600-1639663200@cmsa.fas.harvard.edu SUMMARY:Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formation DESCRIPTION:Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou\, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$\, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation\, which is characterized by the vanishing of the inverse foliation density. In particular\, when the magnetic field is absent in MHD\, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations\, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves\, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations\, we reveal their hidden subtle structures. With them\, we give a complete description of solutions’ dynamics up to the earliest singular event\, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin. URL:https://cmsa.fas.harvard.edu/event/12-16-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211202T130000 DTEND;TZID=America/New_York:20211202T140000 DTSTAMP:20260707T094147 CREATED:20240214T075408Z LAST-MODIFIED:20240304T053731Z UID:10002571-1638450000-1638453600@cmsa.fas.harvard.edu SUMMARY:Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger DESCRIPTION:Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion\, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions. URL:https://cmsa.fas.harvard.edu/event/12-2-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211119T130000 DTEND;TZID=America/New_York:20211119T140000 DTSTAMP:20260707T094147 CREATED:20240214T074604Z LAST-MODIFIED:20240304T053957Z UID:10002570-1637326800-1637330400@cmsa.fas.harvard.edu SUMMARY:On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U(1) Symmetric Spacetimes DESCRIPTION:strong>Abstract: The analysis of global structure of the Einstein equations for general relativity\, in the context of the initial value problem\, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome\, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational\, fixed-point free\, spatial U(1) isometry group are globally well-posed. In our previous works\, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk\, after discussing some preliminaries and background\, we shall discuss about yet another structure of the U(1) symmetric Einstein equations\, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations. URL:https://cmsa.fas.harvard.edu/event/11-19-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211111T130000 DTEND;TZID=America/New_York:20211111T140000 DTSTAMP:20260707T094147 CREATED:20240214T074127Z LAST-MODIFIED:20240304T054620Z UID:10002567-1636635600-1636639200@cmsa.fas.harvard.edu SUMMARY:Sharp decay for Teukolsky equation in Kerr spacetimes DESCRIPTION:Abstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components\, $s=0\, \pm 1\, \pm 2$ corresponding to the scalar field\, the Maxwell field\, and the linearized gravity\, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes. URL:https://cmsa.fas.harvard.edu/event/11-11-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211104T130000 DTEND;TZID=America/New_York:20211104T140000 DTSTAMP:20260707T094147 CREATED:20240214T073728Z LAST-MODIFIED:20240304T054749Z UID:10002565-1636030800-1636034400@cmsa.fas.harvard.edu SUMMARY:The stability of charged black holes DESCRIPTION:Abstract: Black holes solutions in General Relativity are parametrized by their mass\, spin and charge. In this talk\, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally\, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole\, where the interaction between the radiations prevents the separability in modes. URL:https://cmsa.fas.harvard.edu/event/11-4-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211028T093000 DTEND;TZID=America/New_York:20211028T103000 DTSTAMP:20260707T094147 CREATED:20240213T112817Z LAST-MODIFIED:20240304T102039Z UID:10002500-1635413400-1635417000@cmsa.fas.harvard.edu SUMMARY:The classical interior of charged black holes with AdS asymptotics DESCRIPTION:Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations\, Cauchy horizons never form. We then consider charged scalars\, which are known to condense at low temperatures\, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity\, and there is no Cauchy horizon. Before reaching the singularity\, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion\, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations\, the number of Kasner inversions depends very sensitively on temperature\, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures\, the final Kasner exponent exhibits fractal-like behavior. URL:https://cmsa.fas.harvard.edu/event/10-28-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211022T093000 DTEND;TZID=America/New_York:20211022T103000 DTSTAMP:20260707T094147 CREATED:20240213T105511Z LAST-MODIFIED:20240304T101145Z UID:10002466-1634895000-1634898600@cmsa.fas.harvard.edu SUMMARY:The Large D Limit of Einstein’s Equations DESCRIPTION:Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study\, with relatively simple techniques\, some of the thorniest problems in black hole physics\, such as the non-linear evolution of the instabilities of black strings and black branes\, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about\, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394. URL:https://cmsa.fas.harvard.edu/event/10-22-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211015T103000 DTEND;TZID=America/New_York:20211015T113000 DTSTAMP:20260707T094147 CREATED:20240125T164122Z LAST-MODIFIED:20240125T164122Z UID:10001336-1634293800-1634297400@cmsa.fas.harvard.edu SUMMARY:General Relativity 2021-22 DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a seminar on General Relativity\, organized by Aghil Alaee\, Jue Liu\, Daniel Kapec\, and Puskar Mondal. This seminar will take place on Thursdays at 9:30am – 10:30am (Eastern time). The meetings will take place virtually on Zoom. To learn how to attend\, please fill out this form. \nThe schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n2/10/2022\nTin Yau Tsang (UC Irvine)\nTitle: Dihedral ridigity and mass \nAbstract: To characterise scalar curvature\, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk\, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).\n\n\n2/17/2022\nShiraz Minwalla\n(Tata Institute of Fundamental Research\, Mumbai)\nTitle: Black Hole dynamics at Large D \nAbstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics\, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.\n\n\n2/24/2022\nAchilleas Porfyriadis\n(Harvard Black Hole Initiative)\nTitle: Extreme Black Holes: Anabasis and Accidental Symmetry \nAbstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2) transformation properties of the spherically symmetric linear perturbations of\nAdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2\, with or without additional matter\, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of  AdS_2.\n\n\n3/10/2022\nDavid Fajman (University of Vienna)\nTitle: The Einstein-flow on manifolds of negative curvature\n\nAbstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes\, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations\, how they can be handled depending on the matter model at hand\, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.\n\n\n3/21/2022\nProf. Arick Shao (Queen Mary University of London)\nTitle: Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes \nAbstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation\, we prove rigorous mathematical statements toward this conjecture. \nIn particular\, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result\, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes. \nThis is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).\n\n\n3/24/2022\nQian Wang\, University of Oxford\nTitle: Rough solutions of the $3$-D compressible Euler equations \nAbstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D\, for the Cauchy data of the velocity\, density and vorticity $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $22$. At the opposite extreme\, in the incompressible case\, i.e. with a constant density\,  the result is known to hold for $\omega\in H^s$\, $s>3/2$ and fails for $s\le 3/2$\, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $s>2\, \\, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves\, governed by quasilinear wave equations\, and vorticity which is transported by the flow. To overcome this difficulty\, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.\n\n\n3/28/2022\nEmanuele Berti\, Johns Hopkins University\nTitle: Black Hole Spectroscopy \nAbstract: According to general relativity\, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes\, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as\, say\, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?\n\n\n4/7/2022\n\nCMSA General Relativity Conference\n\n\n4/14/2022\nChao Liu\, Huazhong University of Science and Technology\nTitle: Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4 \nAbstract: In this talk\, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.\n\n\n4/21/2022\nJinhua Wang\,\nXiamen University\nTitle: Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system \nAbstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability\, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof\, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover\, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.\n\n\n4/28/2022\nAllen Fang\, Sorbonne University\nTitle: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter \nAbstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk\, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/10/2021 \n(10:30am – 11:30am (Boston time)\nPhilippe G. LeFloch\, Sorbonne University and CNRS\nTitle: Asymptotic localization\, massive fields\, and gravitational singularities \nAbstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First\, the Seed-to-Solution Method for Einstein’s constraint equations\, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass\, Schwarzschild decay\, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second\, the Euclidian-Hyperboloidal Foliation Method\, introduced in collaboration with Yue Ma\, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third\, in collaboration with Bruno Le Floch and Gabriele Veneziano\, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and\, by analyzing Einstein’s constraint equations\, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org\n\n\n9/17/2021 \n(10:30am – 11:30am (Boston time)\nIgor Rodnianski\, Princeton University\nTitle: Stable Big Bang formation for the Einstein equations \nAbstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature\, going back more than 50 years\, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data\, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents\, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.\n\n\n9/24/2021 \n(10:30am – 11:30am (Boston time)\nAlex Lupsasca\nTitle: On the Observable Shape of Black Hole Photon Rings \nAbstract: The photon ring is a narrow ring-shaped feature\, predicted by General Relativity but not yet observed\, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice\, near-term interferometric observations may be limited to the visibility amplitude alone\, which contains incomplete shape information: for convex curves\, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths\, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.\n\n\n10/1/2021 \n(10:30am – 11:30am (Boston time)\nZhongshan An\, University of Connecticut\nTitle: Static vacuum extensions of Bartnik boundary data near flat domains \nAbstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation\, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.\n\n\n10/8/2021 \n(10:30am – 11:30am (Boston time)\nXiaoning Wu\, Chinese Academy of Sciences\nTitle: Causality Comparison and Postive Mass \nAbstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper\, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new\, substantially simple\, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity\n\n\n10/15/2021 \n(10:30am – 11:30am (Boston time)\nJiong-Yue Li\, Sun Yat-Sen University\nTitle: Peeling properties of the spinor fields and the solutions to nonlinear Dirac equations \nAbstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint\, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism\, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.\n\n\n10/22/2021 \n(11:00am – 12:30pm (Boston time)\nRoberto Emparan\, University of Barcelona\nTitle: The Large D Limit of Einstein’s Equations \nAbstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study\, with relatively simple techniques\, some of the thorniest problems in black hole physics\, such as the non-linear evolution of the instabilities of black strings and black branes\, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about\, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.\n\n\n10/28/2021\nJorge Santos\, University of Cambridge\nTitle: The classical interior of charged black holes with AdS asymptotics \nAbstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations\, Cauchy horizons never form. We then consider charged scalars\, which are known to condense at low temperatures\, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity\, and there is no Cauchy horizon. Before reaching the singularity\, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion\, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations\, the number of Kasner inversions depends very sensitively on temperature\, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures\, the final Kasner exponent exhibits fractal-like behavior.\n\n\n11/4/2021\nat 10 am ET\nElena Giorgi\, Columbia University\nTitle: The stability of charged black holes \nAbstract: Black holes solutions in General Relativity are parametrized by their mass\, spin and charge. In this talk\, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally\, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole\, where the interaction between the radiations prevents the separability in modes.\n\n\n11/11/2021\n*9:30 am ET*\nSiyuan Ma\, Sorbonne University\nTitle: Sharp decay for Teukolsky equation in Kerr spacetimes \nAbstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components\, $s=0\, \pm 1\, \pm 2$ corresponding to the scalar field\, the Maxwell field\, and the linearized gravity\, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.\n\n\n11/19/2021 \n(10:30–11:30 am ET)\nNishanth Gudapati\, Clark University\nTitle: On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U(1) Symmetric Spacetimes \nAbstract: The analysis of global structure of the Einstein equations for general relativity\, in the context of the initial value problem\, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome\, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational\, fixed-point free\, spatial U(1) isometry group are globally well-posed. In our previous works\, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk\, after discussing some preliminaries and background\, we shall discuss about yet another structure of the U(1) symmetric Einstein equations\, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.\n\n\n12/2/2021\nProfessor Geoffrey Comp\nére\, Université Libre de Bruxelles\nTitle: Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger \nAbstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion\, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.\n\n\n12/16/2021\nXinliang An\, University of Singapore\nTitle: Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formation \nAbstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou\, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$\, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation\, which is characterized by the vanishing of the inverse foliation density. In particular\, when the magnetic field is absent in MHD\, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations\, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves\, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations\, we reveal their hidden subtle structures. With them\, we give a complete description of solutions’ dynamics up to the earliest singular event\, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin. URL:https://cmsa.fas.harvard.edu/event/general-relativity-2021-22/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211015T093000 DTEND;TZID=America/New_York:20211015T103000 DTSTAMP:20260707T094147 CREATED:20240213T105113Z LAST-MODIFIED:20240304T101004Z UID:10002463-1634290200-1634293800@cmsa.fas.harvard.edu SUMMARY:Peeling properties of the spinor fields and the solutions to nonlinear Dirac equations DESCRIPTION:Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint\, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism\, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models. URL:https://cmsa.fas.harvard.edu/event/10-15-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211008T093000 DTEND;TZID=America/New_York:20211008T103000 DTSTAMP:20260707T094147 CREATED:20240213T110012Z LAST-MODIFIED:20240304T101810Z UID:10002469-1633685400-1633689000@cmsa.fas.harvard.edu SUMMARY:Causality Comparison and Postive Mass DESCRIPTION:Speaker: Xiaoning Wu\, Chinese Academy of Sciences \nTitle: Causality Comparison and Postive Mass \nAbstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper\, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new\, substantially simple\, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity URL:https://cmsa.fas.harvard.edu/event/10-8-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211001T093000 DTEND;TZID=America/New_York:20211001T103000 DTSTAMP:20260707T094147 CREATED:20240304T101543Z LAST-MODIFIED:20240304T101543Z UID:10002898-1633080600-1633084200@cmsa.fas.harvard.edu SUMMARY:Static vacuum extensions of Bartnik boundary data near flat domains DESCRIPTION:Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation\, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang. URL:https://cmsa.fas.harvard.edu/event/10-1-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20210924T093000 DTEND;TZID=America/New_York:20210924T103000 DTSTAMP:20260707T094147 CREATED:20240213T113915Z LAST-MODIFIED:20240304T100711Z UID:10002510-1632475800-1632479400@cmsa.fas.harvard.edu SUMMARY:9/24/2021 General Relativity Seminar DESCRIPTION:Title: On the Observable Shape of Black Hole Photon Rings \nAbstract: The photon ring is a narrow ring-shaped feature\, predicted by General Relativity but not yet observed\, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice\, near-term interferometric observations may be limited to the visibility amplitude alone\, which contains incomplete shape information: for convex curves\, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths\, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements. URL:https://cmsa.fas.harvard.edu/event/9-24-2021-general-relativity-seminar/ CATEGORIES:General Relativity Seminar END:VEVENT END:VCALENDAR